For satellite-aided positioning systems or global navigation satellite systems (GNSS), particularly the Global Positioning System (GPS), the multiple reference station RTK approach is widely known as a differential method for combining the data from a regional reference station network to provide precise measurement correction to users in the field. This is performed by measuring the regional errors at the reference station locations and interpolating them for the location of the rover. The quality of those corrections is dependent on the reference station spacing, the location of the rover, and the characteristics of the measurement errors.
Generally, the quality of Network RTK corrections is a function of the following factors: network geometry, measurement errors, elimination of nuisance parameters (i.e. ambiguities), and the interpolation model that is used. All of these aspects are intermixed, for example, the interpolation model that is used should have the same spatial shape as the measurement errors. Alternatively, if the measurement errors are uniform then the reference stations can be located further away than if the measurement errors are not uniform.
The factors that affect Network RTK performance are generally focused around the qualities and characteristics of the measurement errors. An accurate understanding of the measurement errors leads to an optimal interpolation model and network geometry for a given level of desired rover performance.
In some of the more advanced cases of prior art the measurement error properties are extrapolated using network geometry to predict the performance for the rover in addition to the performance of the network. Many quality indicators for network RTK use the residual errors measured by the network reference stations to derive the current error conditions and characteristics. These characteristics are compared against the current interpolation model to determine the model residuals. For example, if the measured network residuals are linear and a linear interpolation model is used then there is a high likelihood that the rover will experience a high level of performance. The model residuals can then be used to predict the model inaccuracies as a function of the distance to the nearby reference stations. For example, if the model residuals are high but the rover is at a reference station then the model errors have no effect.
The ability to determine the model residuals is a function of the degrees of freedom of the interpolation model. If there are no degrees of freedom then no residuals can be determined. In this case degrees of freedom can be created by excluding one of the reference stations from the model calculation.
Network-Based RTK methods use a network of reference stations to measure the correlated error over a region and to predict their effects spatially and temporally within the network. Although the name suggests that these methods are real-time specific, they can also be used in postmission analysis. This process can reduce the effects of the correlated errors much better than the single reference station approach, thus allowing for reference stations to be spaced much further apart thereby covering a larger service area than the traditional approach, while still maintaining the same level of rover performance.
Network RTK is comprised of six main processes:    1. Processing of the reference station data to resolve the network ambiguities,    2. Selection of the reference stations that will contribute to the corrections for the rover,    3. Generation of the network corrections,    4. Interpolation of the corrections for the rover's location,    5. Formatting and transmission of the corrections and    6. Computation of the rover position.
The main task of the network computation is to resolve the ambiguities for all stations in the network to a common ambiguity level, such that the bias caused by the ambiguities is cancelled when double differences are formed. The network correction computation uses the ambiguity levelled phase observations from the network reference stations to precisely estimate the differential correlated errors for the region.
A subset of stations from the reference network, known as a cell, is selected to generate the correction for the rover based on the rover's position. One station in the cell, usually the one closest to the rover, is selected as the master station. The correction interpolation process models the network corrections to determine the effects of the correlated errors at the rover's position. Depending on the correction concept (Master Auxiliary, VRS or FKP), the interpolation may be done either by the reference station software or the rover itself. The corrections are formatted in such a way that the rover or standard RTK software can interpret them.
In U.S. Pat. No. 5,323,322 a networked differential GPS system is disclosed that provides interpolations of reference station corrections tailored for particular user locations between the reference stations. Each reference station takes real-time ionospheric measurements with codeless cross-correlating dual-frequency carrier GPS receivers and computes real-time orbit ephemeredes independently. An absolute pseudo-range correction (PRC) is defined for each satellite as a function of a particular user's location. A map of the function is constructed, with “iso-PRC” contours, wherein the network measures the PRCs at a few points, so-called reference stations and constructs an iso-PRC map for each satellite. Corrections are interpolated for each user's site on a subscription basis. Although a central processing facility comprising means for generating quality control information by using over-specified reference station information and applying a root-sum-squares algorithm is disclosed, no further specification of the quality control information is given and no map like representation is specified.
The GPS satellites currently transmit ranging signals on two frequencies L1 and L2. The ranging signal consists of unambiguous code measurements and ambiguous, but higher precision, phase measurements. The L1 and L2 code or phase measurements may be transformed into dispersive (or ionospheric) and non-dispersive (or geometric) values using the geometry free linear combination and the ionosphere free linear combination respectively,
            Φ      dispersive        =                            f                      L            ⁢                                                  ⁢            2                    2                                      f                          L              ⁢                                                          ⁢              2                        2                    -                      f                          L              ⁢                                                          ⁢              1                        2                              ⁢              (                              Φ                          L              ⁢                                                          ⁢              1                                -                      Φ                          L              ⁢                                                          ⁢              2                                      )                        Φ              non        -        dispersive              =                  1                              f                          L              ⁢                                                          ⁢              1                        2                    -                      f                          L              ⁢                                                          ⁢              2                        2                              ⁢              (                                            f                              L                ⁢                                                                  ⁢                1                            2                        ⁢                          Φ                              L                ⁢                                                                  ⁢                1                                              -                                    f                              L                ⁢                                                                  ⁢                2                            2                        ⁢                          Φ                              L                ⁢                                                                  ⁢                2                                                    )            where ΦL1 and ΦL2 are the raw measured code or phase measurements in meters for the L1 and L2 signals respectively, Φdispersive is the dispersive code or phase measurements in meters, Φnon-dispersive is the non-dispersive code or phase measurements in meters and fL1 and fL2 are the frequencies in Hz of the L1 and L2 signals respectively. See e.g. RTCM (2007) “RTCM Standard 10403.1 Differential GNSS (Global Navigation Satellite Systems) Services—Version 3 With Amendment 1”, Radio Technical Commission for Maritime Services, 27 Oct. 2007, page 3-29. Euler, H-J. and Zebhauser, B. E. (2003): “The Use of Standardized Network RTK Messages in Rover Applications for Surveying”, Proc. Of ION NTM 2003, Jan. 22-24, 2003, Anaheim, Calif. explain how such network RTK positioning can be achieved using the Master Auxiliary Concept and how sending dispersive and non-dispersive corrections at different rates can magnify the measurement noise. However, this paper does not include how a quality indicator may be calculated that is able to predict the level of residual error after the corrections are applied or the performance of the rover. This paper summarises the basic theory that is the foundation of the Master Auxiliary Concept, namely the idea of a common ambiguity level and the representation of the network corrections as dispersive and non-dispersive correction differences, and provides an example of how these correction differences can be interpolated for a particular rover location. The theory is also useful as background to this invention which describes the quality of the corrections for a set of arbitrary rover locations and which is also derived from ambiguity levelled phase ranges.
In Wanninger, L. (2004): “Ionospheric Disturbance Indices for RTK and Network RTK Positioning”, Proc. of ION GNSS 2004, Long Beach, Calif. an approach with an ionospheric Network RTK index I95L is disclosed where the index is computed from a 4 station sub-network with the ionospheric correction model being based on the observations of 3 surrounding reference stations and a fourth station being used as a monitor station. However, the approach provides only an index without calculation of values for a given rover location. Further, the index does not apply to the non-dispersive, i.e. troposphere and geometry component. Wübbena, G., Schmitz, M., Bagge, A. (2004) “GNSMART Irregularity Readings for Distance Dependent Errors”, White Paper, Geo++, mention the ionospheric delay of GNSS observations as the major error source in the atmosphere, which results into a dependency of a GNSS user from the separation to a reference station. Therefore, focus is placed on the ionospheric error component with an irregularity proposed as an indicator to decide on processing strategies on a RTK rover system in the field. However, the approach is based on per satellite residuals and does not calculate values for a given rover location. The distance based irregularity parameter is discontinuous and applies only to the dispersive component.
Two different ionospheric linearity indicators to predict Network RTK performance are proposed in Chen, X., Landau, H., Vollath, U., (2003) “New Tools for Networked RTK Integrity Monitoring”, ION GPS/GNSS 2003, Sep. 9-12, 2003, Portland, Oreg. The ionospheric residual integrity monitoring omits one reference station from interpolation and then compares the interpolation results at that station with the real measurements. It computes a weighted RMS over all satellites which can also be considered as integrity monitoring for residual interpolation and ambiguity resolution in the network. The ionospheric residual interpolation uncertainty as second indicator uses sufficient surrounding reference stations and produces standard deviation of interpolation with an interpolation method such as weighted linear interpolation method. The standard deviation represents the ionospheric linearity over the interpolation region for the field user. In this document it is also proposed to use similar indicators that can be used for the non-dispersive part. However, neither non-dispersive errors are disclosed in detail nor are equations specified. The values are generated when a position (latitude, longitude and height) is received from a rover. This requires the rover to determine the height and to transmit the information. Further, the model is discontinuous, i.e. artificial irregularities do exist between different parts of the network, and does not use the data of the whole network in the calculation of the quality estimates. The representation is based on the distance and change in height from a single reference station.
An overview of prior art is also given in Alves, P., Geisler, I., Brown, N., Wirth, J. and Euler, H.-J. (2005) “Introduction of a Geometry-Based Network RTK Quality Indicator”, GNSS 2005, Dec. 8-10, 2005, Hong Kong. In this document also a network RTK quality indicator based on the characteristics of the measurement errors is introduced. The indicator assumes that the more linear the regional correlated errors, the better the interpolation methods will perform. The linearity of the network measurement errors is measured and weighted based on the distance to the rover. However, the approach also is discontinuous and does not use the data of the whole network in the calculations. It does not apply to the non-dispersive component and does not use height information.